\begin{answer}
We have
$$
\begin{aligned}
p(y=1|x, \phi, \mu_0, \mu_1, \Sigma) &= \frac{p(x|y=1)p(y=1)}{p(x|y=1)p(y=1) + p(x|y=0)p(y=0)}\\
&= \frac{1}{1 + \frac{p(x|y=0)p(y=0)}{p(x|y=1)p(y=1)}}\\
&= \frac{1}{1 + \exp(-\frac{1}{2}[(x - \mu_0)^T\Sigma^{-1}(x - \mu_0) -(x - \mu_0)^T\Sigma^{-1}(x - \mu_0)])}\frac{1 - \phi}{\phi}\\
&= \frac{1}{1 + \exp(-[(\mu_1 - \mu_0)^T\Sigma^{-1}x  ) + \frac{1}{2}(\mu_0^T\Sigma^{-1}\mu_0 - \mu_1^T\Sigma^{-1}\mu_1) - \log\frac{1-\phi}{\phi}]}
\end{aligned}
$$

So we can take 

$$
\theta = (\mu_1 - \mu_0)^T\Sigma^{-1},\\ 
\theta_0 = \frac{1}{2}(\mu_0^T\Sigma^{-1}\mu_0 - \mu_1^T\Sigma^{-1}\mu_1) - \log\frac{1-\phi}{\phi}
$$

\end{answer}
